C varies inversely as J. If C = 7 when J = 0.7, determine C when J = 12
C varies inversely as J ---> C = k(1/J) , where k is a constant
when C=7, J=.7
7 = k(1/.7)
k = 4.9
so C = 4.9/J
when J=12
C = 4.9/12 = .408333..
or:
C1/C2 = J2/J1
7/C2 = 12/.7
12C2 = 7(.7)
C2 = 7(.7)/12 = .408333..
notice the actual calculations are of course the same.
Well, let's clown around with these inverse variables! If C varies inversely as J, that means the product of C and J should remain constant.
So, let's find that constant value using the initial values of C and J: C = 7 and J = 0.7. The product of these values is: C × J = 7 × 0.7 = 4.9.
Now, to find C when J = 12, we can set up another equation using the same constant: C × J = 4.9. Plugging in J = 12, we get: C × 12 = 4.9.
To solve for C, we divide both sides of the equation by 12: C = 4.9 ÷ 12 = 0.4083333333333333.
So, when J = 12, C is approximately 0.4083333333333333. Don't worry if C seems like a small number - it's all part of the clowning around of inverse variation!
To determine the value of C when J = 12, we can use the concept of inverse variation. Inverse variation states that when two variables are inversely proportional, their product remains constant.
We are given that C varies inversely as J, which can be written as:
C ∝ 1/J
To find the constant of variation, we can use the initial values given in the problem. When C = 7 and J = 0.7, we can write:
C * J = k
Solving for k:
7 * 0.7 = k
4.9 = k
Now we have the constant of variation, which is 4.9. We can use this constant to find the value of C when J = 12:
C * J = k
C * 12 = 4.9
Dividing both sides of the equation by 12:
C = 4.9 / 12
C ≈ 0.408
Therefore, when J = 12, C is approximately 0.408.
To solve this problem, we need to understand what it means for two variables to vary inversely. When two variables vary inversely, it means that as one variable increases, the other variable decreases proportionally, and vice versa.
In this case, C varies inversely as J. Mathematically, we can represent this relationship with the equation C = k/J, where k is a constant of proportionality.
To find the value of k, we can substitute the given values of C and J into the equation and then solve for k.
When C = 7 and J = 0.7, the equation becomes:
7 = k/0.7
To solve for k, we can multiply both sides of the equation by 0.7:
7 * 0.7 = k
k = 4.9
Now that we have the value of k, we can use it to find C when J = 12. Substituting into the equation again, we have:
C = 4.9/12
Simplifying, we find:
C = 0.4083
Therefore, when J = 12, C is approximately 0.4083.